Problem: What do the following two equations represent? $-2x+4y = 5$ $6x-12y = 3$
Putting the first equation in $y = mx + b$ form gives: $-2x+4y = 5$ $4y = 2x+5$ $y = \dfrac{1}{2}x + \dfrac{5}{4}$ Putting the second equation in $y = mx + b$ form gives: $6x-12y = 3$ $-12y = -6x+3$ $y = \dfrac{1}{2}x - \dfrac{1}{4}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.